A Bound for the Distribution of the Hitting Time of Arbitrary Sets by Random Walk
نویسندگان
چکیده
We consider a random walk S n = n i=1 X i with i.i.d. X i. We assume that the X i take values in Z d , have bounded support and zero mean. For A ⊂ Z d , A = ∅, we define τ A = inf{n ≥ 0 : S n ∈ A}. We prove that there exists a constant C, depending on the common distribution of the X i and d only, such that sup ∅∅ =A⊂Z d P {τ A = n} ≤ C/n, n ≥ 1.
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